In common with the work of Schöberl & Zaglmayr [1]}, [2]}, we obtain basis functions with local
complete sequence properties, i.e. on the interior of each cell the discrete
spaces form a subcomplex of the de Rham complex. Our construction of the basis
functions for \(\mathrm {NCE}_p\) , \(\mathrm {NCF}_p\) , and \(\mathrm {DQ}_p\)  from that of \(\mathrm {Q}_p\)  is the same,
but we start from a different basis for \(\mathrm {Q}_p\) ; Schöberl & Zaglmayr start
with integrated Lagrange polynomials on the reference interval, whereas we
employ the FDM element proposed in our previous work [3]}. This
choice yields greater sparsity, because the mass matrix on the reference
interval decouples the interior DOFs.
